关键词: NURBS 曲线, 有理Bé, zier 曲线, toric 退化

Abstract: NURBS curve, as a curve fitting tool, is widely used in geometric modeling. When a
weight approaches to infinity, the limit of NURBS curve tends to corresponding control point.
However, while all the weights tend to infinity, the degeneration of NURBS curve is still unknown. In
this paper, we converts the NURBS curve to piecewise rational Bézier curves by knot insertion
algorithm and obtain the degeneration of NURBS curve while all the weights approach to infinity by
using the degenerations of rational Bézier curves.

Key words: NURBS curve, rational Bézier curve, toric degeneration